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Key Components of the Standards Focus and coherence • A focus on key topics at each grade level • Coherent progressions across grade levels Balance of concepts and skills • Requirement of both conceptual understanding and
procedural fluency in the content standards Mathematical practices • Reasoning and sense-making in mathematics College and career readiness • Ambitious but achievable level
3 www.corestandards.org
Precursors to the Practice Standards
Principles and Standards for School Mathematics
Process Standards • Problem Solving • Reasoning • Communication • Connections • Representation
Adding It Up
Strands • Conceptual Understanding • Procedural Fluency • Strategic Competence • Adaptive Reasoning • Productive Disposition
4 NCTM 2000 NRC 2001
Standards for Mathematical Practice
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
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5 Pillars for Mathematics Reasoning to make sense of mathematics Productive use of discourse when explaining and justifying mathematical thinking Procedural fluency Flexible and appropriate use of mathematical representations Confidence and perseverance in solving problems
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Course 1 Focus Pillar Practices
1. Reasoning to make sense of mathematics
1. Make sense of problems and persevere in solving them.
8. Look for and make use of structure.
9. Look for and express regularity in repeated reasoning.
2. Productive use of discourse when explaining and justifying mathematical thinking
3. Construct viable arguments and critique the reasoning of others.
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Which Does Not Belong?
Why?
Which Does Not Belong?
2, 3, 15, 31
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Why?
Learning Outcomes Learner and the Learning Environment • Characterize problem-solving experiences that require math
reasoning and communication.
• Choose and adapt mathematical tasks and questions to promote deeper levels of student understanding and thinking and prepare students for Next Generation Assessments.
Content Knowledge • Give examples of how the mathematics standards in the
Common Core State Standards exhibit focus and coherence.
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Learning Outcomes Research-Based Instructional Strategies • Explain the role talk has in supporting learning of
mathematics.
Data and Differentiation • Use strategies to help ALL students deepen and
communicate their reasoning.
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Building a Bridge to the Common Core State Standards • Scaffolding Instruction • Using Math Talk • Making Connections Explicit • Modeling the Process of Thinking
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Logical Reasoning and Classroom Discourse
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Positive Influences of Math Discourse
• Talk can reveal understanding and misunderstanding.
• Talk supports robust learning by boosting memory.
• Talk supports deeper reasoning.
• Talk supports language development.
• Talk supports the development of social skills. 14
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Project Challenge Scores on TOMA-2
Beginning After 2 Years
Below Average
0
Average 23%
Above Average
23% 36%
Superior/ Very Superior
4% 41%
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73%
Project Challenge Scores on TOMA-2
Beginning After 2 Years
Below Average
0
Average 23%
Above Average
23% 36%
Superior/ Very Superior
4% 41%
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73%
Talk Moves
• Revoicing • Repeating • Reasoning • Adding on • Waiting
Classroom Discussions: Using Math Talk to Help Students Learn, 2009
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Kindergarten Example: How many students are wearing shoelaces?
• What mathematics are the kindergarteners talking about?
• How does the teacher help Maimouna clarify and share her thoughts?
• How does the teacher help the class orient to the thinking of Maimouna?
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Which is more, nine or five? T: Can you prove it to us?
M: This one is taller than the five because the five is shorter and the nine is bigger.
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Grade 6 Example: Identifying points on a number line
M: Since we already knew that three-fifths would be smaller than three-fourths we would put it more to the left of it (three-fourths) and since we knew that three-fourths was more to the left of A, it would mean that was less, so we knew three-fifths couldn’t be it because it was less than A.
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High Quality Math Talk
“Our goal is not to increase the amount of talk in our classrooms, but to increase the amount of high quality talk in our classrooms—the mathematical productive talk.”
–Classroom Discussions: Using Math Talk to Help Students Learn, 2009
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Comparing Math Tasks
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What are the important elements of mathematical tasks that promote
thinking, reasoning, and communication?
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Asking Essential Questions
What do we want our students to know and understand about money?
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Asking Essential Questions
Money Task 1 I have pennies, dimes, and nickels in my pocket. If I take three coins out of my pocket, what are the different amounts of money I could have taken?
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1. Solve individually, then share your strategies and solutions with your group.
2. Record your strategies and solutions.
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Money Task 2 I have four coins. I have one penny, two nickels, and one quarter. How much money do I have?
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1. Solve individually, then share your strategies and solutions with your group.
2. Record your strategies and solutions.
Group Task
• How are the tasks alike and different?
• How do the tasks compare to the criteria for a worthwhile task?
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Comparing Tasks
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Money Task #1 I have pennies, dimes, and nickels in my pocket. If I take three coins out of my pocket, what are the different amounts of money I could have taken?
Money Task #2 I have four coins. I have one penny, two nickels, and one quarter. How much money do I have?
Knowledge: Conceptual vs. Procedural
Conceptual Knowledge consists of well-defined concepts, more informal mathematical ideas, and relationships among ideas, concepts, and skills.
Procedural Knowledge involves knowledge of facts, symbols, rules, and procedures.
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“It is possible to have procedural knowledge of a topic and to have little or no conceptual knowledge.
However, without knowledge of the important concepts and ideas, it is impossible to truly understand that topic.”
–Classroom Discussions: Using Math Talk to Help Students Learn, 2009
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Knowledge: Conceptual vs. Procedural
Distinguishing Cognitive Levels of Tasks
• Low-cognitive-level tasks
• High-cognitive-level tasks
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Features of Low-Level Tasks
• Involve memorization or reproduction
• Focus on finding the answer rather than developing understanding
• Rarely require explanation beyond a description of procedure
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Features of High-Level Tasks
• They require more of students than simply remembering a fact or reproducing a skill.
• Students can learn by answering the questions, and the teacher can learn about the students from their responses.
• There may be several acceptable answers and/or several methods to obtain the answer.
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The Importance of Reasoning and Discourse in Math
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Standards for Mathematical Practice
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
5 Pillars for Mathematics Reasoning to make sense of mathematics Productive use of discourse when explaining and justifying mathematical thinking Procedural fluency Flexible and appropriate use of mathematical representations Confidence and perseverance in solving problems
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PG page 6
Course 1 Focus Pillar Practices
1. Reasoning to make sense of mathematics
1. Make sense of problems and persevere in solving them.
8. Look for and make use of structure.
9. Look for and express regularity in repeated reasoning.
2. Productive use of discourse when explaining and justifying mathematical thinking
3. Construct viable arguments and critique the reasoning of others.
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Learning Outcomes
Learner and the Learning Environment • Characterize problem-solving experiences that require math
reasoning and communication.
• Choose and adapt mathematical tasks and questions to promote deeper levels of student understanding and thinking and prepare students for Next Generation Assessments.
Research-Based Instructional Strategies • Explain the role talk has in supporting learning of mathematics.
38
PG page 5
Learning Outcomes Content Knowledge • Give examples of how the mathematics standards in the
Common Core State Standards exhibit focus and coherence.
Data and Differentiation • Use strategies to help ALL students deepen and
communicate their reasoning.
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PG page 5
Thank You!
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1. Understand your needs and develop a transition plan
How Can You Prepare?
2. Create awareness among your staff
How Can You Prepare?
June 24 – 27 | ORLANDO www.modelschoolsconference.com
43
General Staff Awareness ELA Teachers Math Teachers Content Area
Teachers
COURSE 1: Driving Student Achievement With the Common Core
COURSE 1: Putting Text First: A Focus on Complexity, Range, and Quality COURSE 2: Building Vocabulary: A Focus on Academic and Domain-Specific Words COURSE 3: Writing Arguments and Conducting Research: A Focus on Using Evidence
COURSE 1: Content Area Literacy: Engaging Students With Complex Text COURSE 2: Academic Language: Building a Bridge to Text-Based Writing COURSE 3: Rigor and Research: Building Writing Proficiency in the Content Areas
COURSE 1: Making Sense of Math: A Focus on Reasoning and Discourse COURSE 2: Mathematical Thinking: A Focus on Representation and Procedural Fluency COURSE 3: Problem Solving: A Focus on Developing Students’ Disposition, Confidence, and Competence
How Can You Prepare?
3. Ongoing PD for teachers & leaders
For more information: [email protected]
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